A logical approach to multilevel security of probabilistic systems

A second-order modal logic for reasoning about multilevel security in probabilistic systems is proposed. A possible world semantics is presented, and it is proved that the logic is sound with respect to it. The semantics is novel in treating probability measures themselves as possible worlds. After giving a syntatic definition of security, it is shown that the semantic interpretation of the syntactic definition is equivalent to an earlier independently motivated characterization called probabilistic noninterference due to J. W. Gray, III (1991). The authors examine a syntatic representation of Gray's applied flow model and discuss the relation between these characterizations of security and between their usefulness in security analysis. A syntatic description of a round-robin server and a sketch of the formal proof of its security are also provided